What Value of p Maximizes the Variance of X?

[TomJerry]

Let the random variable X have the distribution

$P(X=0) = P(=2) = p$

$P(X=1) = 1-2p,$ $0 \le p \le \frac{1}{2}$

For what p is Var X maximum

 

[statdad]

Write down the expression for the variance - it will be a function of p. Maximize that function.